Question and Answers Forum

All Questions      Topic List

Others Questions

Previous in All Question      Next in All Question      

Previous in Others      Next in Others      

Question Number 156270 by Tawa11 last updated on 09/Oct/21

Show that      i    =   sin^(− 1) (((√2)/2))^2     in air, if the refractive  index        n   =   ((sin^2 (60))/(sin^2 (45)))

$$\mathrm{Show}\:\mathrm{that}\:\:\:\:\:\:\mathrm{i}\:\:\:\:=\:\:\:\mathrm{sin}^{−\:\mathrm{1}} \left(\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\right)^{\mathrm{2}} \:\:\:\:\mathrm{in}\:\mathrm{air},\:\mathrm{if}\:\mathrm{the}\:\mathrm{refractive} \\ $$$$\mathrm{index}\:\:\:\:\:\:\:\:\mathrm{n}\:\:\:=\:\:\:\frac{\mathrm{sin}^{\mathrm{2}} \left(\mathrm{60}\right)}{\mathrm{sin}^{\mathrm{2}} \left(\mathrm{45}\right)} \\ $$

Commented by Tawa11 last updated on 10/Oct/21

Sir, I just know that, refractive index,  n    =   ((sin i)/(sin r))

$$\mathrm{Sir},\:\mathrm{I}\:\mathrm{just}\:\mathrm{know}\:\mathrm{that},\:\mathrm{refractive}\:\mathrm{index},\:\:\mathrm{n}\:\:\:\:=\:\:\:\frac{\mathrm{sin}\:\mathrm{i}}{\mathrm{sin}\:\mathrm{r}} \\ $$

Answered by ajfour last updated on 10/Oct/21

n_(air) sin i=n_(medium) sin r  sin i=(n_(medium) /n_(air) )sin r     =nsin r=((sin^2 (60))/(sin^2 (45)))sin r  i=sin^(−1) {((sin^2 (60))/(sin^2 (45)))sin r}

$$\mathrm{n}_{\mathrm{air}} \mathrm{sin}\:\mathrm{i}=\mathrm{n}_{\mathrm{medium}} \mathrm{sin}\:\mathrm{r} \\ $$$$\mathrm{sin}\:\mathrm{i}=\frac{\mathrm{n}_{\mathrm{medium}} }{\mathrm{n}_{\mathrm{air}} }\mathrm{sin}\:\mathrm{r} \\ $$$$\:\:\:=\mathrm{nsin}\:\mathrm{r}=\frac{\mathrm{sin}^{\mathrm{2}} \left(\mathrm{60}\right)}{\mathrm{sin}^{\mathrm{2}} \left(\mathrm{45}\right)}\mathrm{sin}\:\mathrm{r} \\ $$$$\mathrm{i}=\mathrm{sin}^{−\mathrm{1}} \left\{\frac{\mathrm{sin}^{\mathrm{2}} \left(\mathrm{60}\right)}{\mathrm{sin}^{\mathrm{2}} \left(\mathrm{45}\right)}\mathrm{sin}\:\mathrm{r}\right\} \\ $$$$ \\ $$

Commented by Tawa11 last updated on 11/Oct/21

Thanks sir. God bless you.

$$\mathrm{Thanks}\:\mathrm{sir}.\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}. \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com